Summary

This project seeks to improve on the Howard et al. (2020) methods used to estimate sport fish harvest, catches and releases of rockfish in Alaska waters. This is essentially a Bayesian version of the Howard methods that allows for more appropriate and defensible sharing of information between areas, handles missing data in a more appropriate manor, accurately propagates uncertainty throughout the estimation procedure and thus does not rely on the decision tree approach in the original Howard methods. Furthermore, the Bayesian approach should provide sport fish harvest, catch and mortality estimates back to 1978 when the SWHS was implemented. Harvest estimates should be mostly consistent with Howard estimates during contemporary times, but may differ based on more appropriate weighting of SWHS and logbook data, including estimating and correcting bias in the SWHS data. Furthermore, the Howard methods are wholly reliant on logbook release estimates and ignore the release estimates from the SWHS data (inferred from the catch and harvest estimates). Here we explore several models that attempt to balance all of the data in estimating releases.

Data

Harvest data was available for 22 commercial fishing management areas in Southcentral and Southeast Alaska. Areas with negligible rockfish harvest were pooled with adjacent areas for analysis. Specifically the Aleutian and Bering areas were pooled into an area labeled BSAI; the IBS and EKYT were pooled into an area labeled EKYKT; the Southeast, Southwest, SAKPEN and Chignik areas were pooled into an area labeled SOKO2PEN and the Westside and Mainland areas were pooled into an area labeled WKMA.

Stateside Harvest Survey (SWHS)

Statewide harvest survey estimates of rockfish catch and harvest are available for 28 years (1996-2023) for all users and for 13 years (2011-2023) for guided anglers (Figure 0). Additionally, there are estimates from 1977- 1995 that required some partitioning work to ascribe to current management units. Harvests in unknown areas were apportioned based on harvest proportions in 1996. Variance estimates are not available for pre-1996 data and as such, the maximum observed coefficient of variation (cv) in each commercial fisheries management unit was applied.

**Figure 0.**- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.

Figure 0.- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.


SWHS estimates are believed to be biased to some degree. These modelling efforts aim to estimate and correct for that bias with the assumption that logbook harvests are a census of guided harvests.

Rockfish release estimates are inferred from the difference between catch and harvest estimates.

Adam noted that the first 5 years (23 years counting the historical data) in the SWHS data set for PWSO seem unreasonable (close to zero and not corroborated with logbook estimates). Adam recommended setting these harvests to unknown, but current model development has included the data. Once a satisfactory model has been identified we will exam the effects of censoring the PWSO data.

Creel Surveys

NA

Guide Logbooks

Sport fishing guides were required to report their harvest of rockfish for 26 years (1998-2023). Reported harvest is also available by assemblage (pelagic vs. non-pelagic). Harvest of yelloweye and “other” (non-pelagic, non-yelloweye) rockfish were reported separately beginning in 2006.

Logbooks also record the number of rockfish released for the same categories. However, the reliability of the release data is somewhat questionable as reported releases are generally far lower than that estimated by the SWHS. As such several treatments of the data are considered.

Logbook versus SWHS estimates

Estimates of guided harvests and releases from the SWHS do not align with the census from charter logbooks. Logbook harvest reports are generally considered reliable and are used to assess the bias in SWHS reports. However, there is even greater disparity between release estimates in the two sources and it is debatable whether logbook releases should be treated as a census. The Howard et al. (2020) methods do treat the logbook release data as “true” and thus are considerably less than would be estimated from the SWHS data.

**Figure 1.**- SWHS harvest estimates from guided trips (Hhat) versus repoted harvests from charter logbooks (H_lb).

Figure 1.- SWHS harvest estimates from guided trips (Hhat) versus repoted harvests from charter logbooks (H_lb).


The Howard methods treat the logbook release data as a census and then use the ratio of guided:unguided releases in the SWHS to expand the logbook release estimates to generate total and unguided estimates.

To evaluate this discrepancy, several models were used to estimate releases in this exploration. One method (\(LB_{fit}\)) considers the logbook release data to be reliable and a second method (\(LB_{cens}\)) treats the logbook release data as estimates of the minimum released, thus giving more weight to SWHS release estimates. A third method (\(LB_{hyb}\)) is a hybrid approach that treats reported releases of yelloweye as reliable but total rockfish and pelagic rockfish releases as minimums. Model development to date has revealed a tension between the total and pelagic logbook releases and the yelloweye logbook releases.

Composition data

Harvest sampling data exists from Gulf of Alaska areas since 1996 and from Southeast Alaska areas since 2006. Port sampling data is comprised of the number of total rockfish, pelagic and non-pelagic rockfish, black rockfish and yelloweye rockfish.

A current challenge at this juncture is how to accommodate the prohibition on retaining yelloweye in Southeast from 2020 through 2024. Because it is closed to retention the port sampling data is not reflective of releases while remaining an accurate description of the harvest. Current modelling efforts revolve around developing a separate yelloweye curve that censors the missing data.

Process equations

The true harvest \(H_{ay}\) of rockfish for area \(a\) during year \(y\) is assumed to follow a temporal trend defined by a penalized spline:

\[\begin{equation} \textrm{log}(H_{ay})~\sim~\textrm{Normal}(f(a,y), {\sigma_H}) \end{equation}\]

where \(f(a,y)\) in a p-spline basis with 7 components (knots) and a second degree penalty. The variance, \(\sigma_H\), was given a normal prior with a mean and standard deviation of 0.25 and 1, respectively.

Charter and private harvest \(H_{ayu}\) (where u = 1 for charter anglers and u = 2 for private anglers) is a fraction of total annual harvest in each area:

\[\begin{equation} H_{ay1}~=~H_{ay}P_{(user)ay1}\\H_{ay2}~=~H_{ay}(1-P_{(user)ay1}) \end{equation}\]

where \(P_{(user)ay1}\) is the fraction of the annual harvest in each area taken by charter anglers. \(P_{(user)ay1}\) was modeled hierarchically across years as:

\[\begin{equation} P_{(user)ay1}~\sim~\textrm{beta}(\lambda1_a, \lambda2_a) \end{equation}\]

with non-informative priors on both parameters.

Annual black rockfish harvest \(H_{(black)ayu}\) for each area and user group is:

\[\begin{equation} H_{(black)ayu}~=~H_{ayu}P_{(pelagic)ayu}P_{(black|pelagic)ayu} \end{equation}\]

where \(P_{(pelagic)ayu}\) is the fraction of the annual harvest for each area and user group that was pelagic rockfish and \(P_{(black|pelagic)ayu}\) is the fraction of the annual harvest of pelagic rockfish for each area and user group that was black rockfish.

The southeast region also tracks two other non-pelagic rockfish assemblages, demersal shelf rockfish (DSR, which includes yelloweye) and slope rockfish. For the southeast region the harvest of those two assemblages is thus

\[\begin{equation} H_{(DSR)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(DSR|non-pelagic)ayu}\\ H_{(slope)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(slope|non-pelagic)ayu}\\ \end{equation}\]

where \(P_{(DSR|non-pelagic)ayu}\) and \(P_{(slope|non-pelagic)ayu}\) are the fractions of the annual harvest of non-pelagic rockfish for each area and user group that were DSR and slope rockfish, respectively.

Annual yelloweye rockfish harvest \(H_{(yelloweye)ayu}\) for each area and user group is calculated differently for central/Kodiak areas and southeast areas. For central and Kodiak areas yelloweye rockfish harvests are calculated as

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(yelloweye|non-pelagic)ayu} \end{equation}\]

where \(P_{(yellow|non-pelagic)ayu}\) is the fraction of the annual harvest of non-pelagic rockfish for each area and user group that was yelloweye rockfish.

For southeast areas yelloweye harvests are a fraction of the DSR harvests such that

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{(DSR)ayu}P_{(yelloweye|DSR)ayu} \end{equation}\]

The composition parameters \(P_{(comp)ayu}\), were modeled using a logistic curve that would allow hindcasting without extrapolating beyond the limit of observed values such that:

\[\begin{equation} \textrm{logit}(P_{(comp)ayu})~=~\beta1_{(comp)ayu} + \frac{\beta2_{(comp)ayu}}{(1 + exp(\beta3_{(comp)ayu}*(y - \beta4_{(comp)ayu})))} + \beta5_{(comp)ayu}*I(u=private)+re_{(comp)ayu} \end{equation}\]

where the \(\beta\) parameters define the intercept, scaling factor, slope, inflection point and private angler effect, respectively, \(y\) is the year index, \(I(u=private)\) is an index variable which is 1 when the user groups is private and 0 otherwise and \(re_{(comp)ayu}\) is a random effect with a non-informative prior.

The true number of released rockfish \(R_{ayu}\) were based on the proportion of the total catch harvested by area, year, user group and species grouping , \(pH_{(comp)ayu}\). Thus, converting \(H_{(comp)ayu}\) to total catches by user group, \(C_{(comp)ayu}\), with \(pH_{(comp)ayu}\) results in estimates of total releases such that

\[\begin{equation} R_{(comp)ayu}~=~ C_{(comp)ayu} - H_{(comp)ayu} ~=~ \frac{H_{(comp)ayu}}{pH_{(comp)ayu}} - H_{(comp)ayu} \end{equation}\]

with total releases equal to the sum of the compositional releases.

The proportion harvest parameters for \(pH_{(comp)ayu}\) were modeled using a logistic curve that would allow hindcasting based on trends in the data without extrapolating beyond the range of observed values such that

\[\begin{equation} \textrm{logit}(pH_{(pH)ayuc})~=~\beta1_{(pH)ayu} + \frac{\beta2_{(pH)ayuc}}{(1 + exp(\beta3_{(pH)ayuc}*(y - \beta4_{(pH)ayuc})))} + \beta5_{(pH)ayuc}*I(u=private)+re_{(pH)ayuc} \end{equation}\]

A random effect term allowed estimation during the historical period when data is available, but the curve defined by the above equation determined release estimates between 1977 and 1990.

Observation equations

SWHS estimates of annual rockfish harvest \(\widehat{SWHS}_H{ay}\) were assumed to index true harvest:

\[\begin{equation} \widehat{SWHS}_H{ay}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay}b_{ay}), \sigma_{SWHSHay}^2\right) \end{equation}\]

where bias in the SWHS harvest estimates \(b_H{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_H{ay}~\sim~\textrm{Normal}(\mu_H{(b)a}, \sigma_H{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

SWHS estimates of guided angler harvest \(\widehat{SWHS}_H{ay1}\) are related to total harvest by:

\[\begin{equation} \widehat{SWHS}_H{ay1}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay1}b_{ay}), \sigma_{SWHS_{ay1}}^2\right) \end{equation}\]

Reported guide logbook harvest \(\widehat{LB}_H{ay}\) is related to true harvest as:

\[\begin{equation} \widehat{LB}_H{ay}~\sim~\textrm{Poisson}(H_{ay1})\\ \widehat{LB}_H{(pelagic)ay}~\sim~\textrm{Poisson}(H_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_H{(yelloweye)ay}~\sim~\textrm{Poisson}(H_{(yelloweye)ay1})\\ \widehat{LB}_H{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(H_{(nonpel,nonye)ay1})\\ \end{equation}\]

Note that for central and Kodiak areas \(H_{(nonpel,nonye)ay1}\) is equal to the total harvest minus pelagic and yelloweye harvests. For southeast areas \(H_{(nonpel,nonye)ay1}\) is equal to the sum of the DSR and slope harvests minus yelloweye harvests.

SWHS estimates of annual rockfish releases \(\widehat{SWHS}_R{ay}\) were assumed to index true releases in a similar fashion and thus modeled similarly. Because logbook release data is more questionable and demonstrates greater disagreement with SWHS estimates (Figure 1), several approaches have been explored. In the first approach model \(LB_{fit}\) treats the release data as a true census and the releases are related to true releases just as harvests were modeled such that:

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{Poisson}(R_{ay1})\\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{Poisson}(R_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Similar to how harvests were modeled, central and Kodiak \(R_{(nonpel,nonye)ay1}\) was equal to total releases minus pelagic and yelloweye releases while for southeast areas it was equal to the sum of DSR and slope releases minues yelloweye releases.

In the second approach we consider the logbook release data to be a minimal estimate of the true releases. Thus model \(LB_{cens}\) censors the release data (censored data is entered as NA) and treats the reported releases as a minimal number such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(ye)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(ye)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(ye)ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(nonpel,nonye)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(nonpel,nonye)ay}, \infty\right) \end{equation}\]

Model \(LB_{hyb}\) is a hybrid approach that treats the yelloweye releases as a reliable census of yelloweye releases (given the emphasis and ease of recording these fish) but censors the pelagic and total rockfish release estimates such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

SWHS estimates of guided angler release \(\widehat{SWHS}_R{ay1}\) is modeled the same as harvests.

SWHS release bias was modeled differently in the \(LB_{fit}\), \(LB_{cens}\), and \(LB_{hyb}\) models. Because the \(LB_{fit}\) model assumes that logbook release data is true and the poison likelihoods assume a much smaller variance than the large variances associated with the SWHS release estimates, SWHS release estimates \(b_R{ay}\) were modeled independently of the harvest bias \(b_H{ay}\) such that

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

where bias in the SWHS release estimates \(b_R{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

The \(LB_{cens}\) model treats the logbook release data as lower bound on the release estimates and thus the likelihood linking true releases to the SWHS release estimates is dominant. During model development it was apparent that estimating bias in the SWHS data was more difficult and a different structure was employed that assumed bias in SWHS release data followed a similar pattern to that of the harvests but is offset by some area specific amount. In these models \(b_R{ay}\) differed from \(b_H{ay}\) by offset \(Rboff_{a}\) such that

\[\begin{equation} b_R{ay}~=~b_H{ay} + Rboff_{ay} \end{equation}\]

where

\[\begin{equation} Rboff_{a}~\sim~\textrm{Normal}(\mu_{(bR)r}, \sigma_{(bR)r}) \end{equation}\]

such that \(Rboff_{a}\) was modeled hierarchically across region r.

The number of pelagic rockfish sampled in harvest sampling programs \(x_{(pelagic)ayu}\) follow a binomial distribution:

\[\begin{equation} x_{(pelagic)ayu}~\sim~\textrm{Binomial}(P_{(pelagic)ayu}, N_{ayu}) \end{equation}\]

where \(N_{ayu}\) is the total number of rockfish sampled in area \(a\) during year \(y\) form user group \(u\). The number of black rockfish sampled in harvest sampling programs and the number of yellow rockfish sampled modeled analogously with an appropriately substituted \(N\).

Unresolved issues and outstanding questions:

Models detailed in this markdown represent the next step in the modelling process whereby the pH parameters are separated out by species. This approach separates the compositional data that is germaine to the harvests from the release estimates and releases are now based on pH. Additionally, this approach allows the pH parameters to differ between pelagic and yelloweye which is appropriate given regulatory changes as well as fisherman and industry behaviour and is born out in the results. The approach results in great uncertainty around unguided release estimates, but that uncertainty is appropriate given the data. These models handle the yelloweye closures in southeast much more appropriately given that the compositional data is no longer directly applied to the release estimates. These versions of the model are in development and it is unclear whether the \(LB_{cens}\) model would work, but it appears applicable to the \(LB_{fit}\) and \(LB_{hyb}\) approaches.

Other issues include:

  1. Complete convergence has not been achieved and the logistic curve parameters for p_pelagic and p_yellow remain the last sticking point. I think that p_pelagic will resolve with longer chains.
  2. Estimate precision: These models are producing more precise harvest estimates that in Adam’s original model. I am not sure why at this juncture. sigma_H on the spline was switched from a fixed value to a prior centered around that fixed value, but the model estimates are in the same range as the fixed value. Would the number of knots in the spline explain this? 7 knots was settled on during early model fitting when it clearly performed better than fewer or more knots.
  3. Prior choices in general need to be vetted. The priors on the logistic curves are fairly informed in an effort to achieve the desired shapes for hindcasting. Ideally, sensitivity testing would occur but the model is very slow to converge. The beta parameters on the logistic curves have required a lot of work on the priors to reach convergence.
  4. Random effects on pH: These are currently used in the model but because pH isn’t linked to data as the p_comp data is I am not sure what to make of them or if they are appropriate.
  5. Model comparisons: I need to write code for comparing models side by side as well as quantifying the differences between these methods and the Howard methods.

Results

**Figure X.**- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Figure X.- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Estimate comparison

Since previous estimates of rockfish harvest have been produced these first 3 graphs will be used to show how the modeled estimates compare to the estimates produced earlier. For total rockfish the estimates are in general agreement although differences are noted. These estimates should be more reliable because they include both SWHS and guide logbook data, handle variance more appropriately, use hierarchical distributions when data is missing, directly consider observation error and are produced using reproducible research.

**Figure 2.**- Total rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 2.- Total rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 3.**- Total rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 3.- Total rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


Notes from Adam: When looking at only black rockfish the most significant differences are for the Prince William Sound Inside area. I did not spend a great deal of time tracking this down although it looks like the previous version used bad values for \(P_{(black)ayu}\) for at least unguided anglers. For the moment I would ignore the results for BSIA and SOKO2SAP. I think it is possible to give approximate values for these areas but it will require a little more coding which I have yet to do.

**Figure 4.**- Black rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 4.- Black rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


And black rockfish releases…

**Figure 5.**- Black rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 5.- Black rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- Yellow rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Yellow rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- Yellow rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Yellow rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- DSR rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- DSR rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- DSR rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- DSR rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- Slope rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Slope rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- Slope rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Slope rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Model fit

Logbook residuals

**Figure 8.**- Residuals from logbook harvests

Figure 8.- Residuals from logbook harvests


SWHS residuals

**Figure 9.**- Residuals from SWHS harvests.

Figure 9.- Residuals from SWHS harvests.



**Figure 10.**- Residual of SWHS releases

Figure 10.- Residual of SWHS releases

Parameter estimates

P(Charter)

These histograms show the posterior distribution of the mean percent of rockfish harvested by the charter fleet.

**Figure 11.**- Mean percent of harvest by charter anglers.

Figure 11.- Mean percent of harvest by charter anglers.


When considered annually we see the percent of rockfish harvested by the charter fleet follows our data fairly well although we just do not have much information about this ratio. Prior to 2011 the percent charter is confounded with SWHS bias and should be mostly discounted.

**Figure 12.**- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

Figure 12.- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

P(Harvest)

These plots show the fitted logistic line to the proportion of caught rockfish that are harvested. These estimates are used for hindcasting catch estimates based on the harvest data in early years when catch estimates are unavailable.


**Figure 13.**- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 13.- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 13.**- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 13.- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 13.**- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.

Figure 13.- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.


## NULL


## NULL

SWHS bias

Figure 14 shows the mean estimate for SWHS bias. Cook Inlet, North Gulf Coast and North Southeast Inside all look pretty good while most other areas have substantial bias. Prince William Sound Inside has the largest bias.

**Figure 14.**- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 14.- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.


Our estimates of SWHS bias track observations fairly well when he have guided harvest estimates. There are some disturbing trends/patterns seen in the earlier time periods. Often the patterns represent periods where SWHS estimates and guide logbook estimates do not follow the recent relationship. I’m not sure what drives the trends but it seems plausible to me that long-term changes in the ratio of charter and private anglers may be a factor. If Charter/Private ratio information is available in the historical creel data it my be helpful here (particularly for North Southeast Inside and South Southeast outside).

**Figure 15.**- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 15.- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

P(pelagic)

We model the percentage of pelagic rockfish in the harvest because we have the information for charter anglers (via logbooks) starting in 1998. Other than looking at the model estimates you can use Figure 8 to compare the two data streams for pelagic rockfish harvest. In general they are in agreement with major exceptions in Price William Sound inside, Prince William Sound outside (early in the time series) and South Southeast inside.

**Figure 16.**- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 16.- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(black|pelagic)

Note that in Southeast Alaska we only have composition data starting in 2006. Tania dug up old SE data, but it did not provide any useful data for species apportionment.

**Figure 17.**- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 17.- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(yelloweye|non-pelagic / yelloweye|DSR)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

P(DSR|non-pelagic)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

P(slope|non-pelagic)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.



Summary of unconverged parameters:

Table 1. Summary of unconverged parameters including the number (n) and the average Rhat from the unconverged parameters.
parameter n badRhat_avg
beta3_yellow 5 7.506351
beta3_pH 5 3.257052
beta0_black 3 2.179705
beta1_black 9 2.164276
sd_comp 1 1.886289
beta2_yellow 4 1.884836
beta3_black 2 1.814276
beta0_yellow 5 1.592059
beta1_yellow 8 1.432235
beta0_pH 10 1.412355
beta1_pH 14 1.381565
parameter n badRhat_avg
beta1_pelagic 9 1.303260
beta2_pH 14 1.300110
beta0_pelagic 8 1.290769
mu_beta0_pelagic 1 1.249309
beta2_black 3 1.243384
beta2_pelagic 4 1.230003
mu_beta0_pH 1 1.222617
beta3_pelagic 2 1.174083
tau_beta0_yellow 2 1.163201
tau_beta0_pH 1 1.145741
Table 2. Summary of unconverged parameters by area
afognak BSAI CI CSEO eastside EWYKT NG northeast NSEI NSEO PWSI PWSO SOKO2SAP SSEI SSEO WKMA
beta0_black 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0
beta0_pelagic 1 1 1 1 0 0 0 1 0 0 0 1 1 0 1 0
beta0_pH 0 0 1 1 1 0 1 1 0 0 1 1 1 0 0 1
beta0_yellow 0 0 0 1 0 0 0 0 1 1 0 0 0 1 0 1
beta1_black 1 0 1 1 1 0 1 1 1 0 1 0 0 1 0 0
beta1_pelagic 1 1 1 1 0 0 0 1 0 0 0 1 1 0 1 1
beta1_pH 1 1 0 1 1 0 1 1 1 0 1 1 0 0 1 1
beta1_yellow 1 0 1 1 1 0 0 0 1 0 0 1 0 1 0 1
beta2_black 0 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0
beta2_pelagic 0 0 0 1 0 0 1 1 0 0 0 0 0 1 0 0
beta2_pH 1 1 0 1 1 1 1 1 0 0 1 1 1 1 1 1
beta2_yellow 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 1
beta3_black 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0
beta3_pelagic 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0
beta3_pH 0 0 0 1 1 0 0 0 1 0 1 0 1 0 0 0
beta3_yellow 0 0 0 1 1 0 0 0 0 1 0 0 0 1 0 1
mu_beta0_pelagic 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
mu_beta0_pH 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
sd_comp 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
tau_beta0_pH 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
tau_beta0_yellow 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0

Parameter estimates:

Summary Table of Parameter Estimates
Parameter mean sd Lower_CI Median Upper_CI
mu_bc_H[1] -0.132 0.075 -0.269 -0.136 0.030
mu_bc_H[2] -0.098 0.045 -0.175 -0.101 0.004
mu_bc_H[3] -0.430 0.072 -0.567 -0.431 -0.284
mu_bc_H[4] -0.995 0.193 -1.387 -0.990 -0.622
mu_bc_H[5] 0.921 0.958 -0.172 0.712 3.473
mu_bc_H[6] -2.157 0.316 -2.753 -2.162 -1.533
mu_bc_H[7] -0.464 0.111 -0.691 -0.462 -0.251
mu_bc_H[8] 0.260 0.385 -0.347 0.226 1.086
mu_bc_H[9] -0.292 0.132 -0.547 -0.291 -0.036
mu_bc_H[10] -0.110 0.067 -0.237 -0.112 0.027
mu_bc_H[11] -0.124 0.038 -0.196 -0.125 -0.046
mu_bc_H[12] -0.252 0.106 -0.469 -0.251 -0.048
mu_bc_H[13] -0.134 0.078 -0.279 -0.135 0.021
mu_bc_H[14] -0.297 0.096 -0.499 -0.295 -0.119
mu_bc_H[15] -0.341 0.051 -0.438 -0.342 -0.242
mu_bc_H[16] -0.251 0.370 -0.881 -0.286 0.588
mu_bc_R[1] 1.310 0.143 1.034 1.309 1.608
mu_bc_R[2] 1.450 0.096 1.262 1.452 1.637
mu_bc_R[3] 1.391 0.141 1.112 1.395 1.661
mu_bc_R[4] 0.918 0.201 0.484 0.925 1.294
mu_bc_R[5] 1.136 0.470 0.216 1.141 2.053
mu_bc_R[6] -1.590 0.424 -2.422 -1.593 -0.757
mu_bc_R[7] 0.288 0.189 -0.082 0.286 0.661
mu_bc_R[8] 0.552 0.201 0.144 0.555 0.934
mu_bc_R[9] 0.342 0.209 -0.113 0.359 0.713
mu_bc_R[10] 1.332 0.136 1.052 1.339 1.583
mu_bc_R[11] 1.038 0.096 0.845 1.037 1.233
mu_bc_R[12] 0.822 0.206 0.408 0.823 1.212
mu_bc_R[13] 1.029 0.105 0.822 1.029 1.232
mu_bc_R[14] 0.909 0.141 0.611 0.910 1.169
mu_bc_R[15] 0.777 0.112 0.554 0.776 0.994
mu_bc_R[16] 1.089 0.126 0.836 1.089 1.337
tau_pH[1] 5.265 0.447 4.432 5.262 6.180
tau_pH[2] 1.942 0.800 0.753 2.265 3.057
tau_pH[3] 2.318 0.259 1.857 2.304 2.862
beta0_pH[1,1] 0.516 0.178 0.154 0.518 0.854
beta0_pH[2,1] 1.329 0.186 0.951 1.342 1.662
beta0_pH[3,1] 1.413 0.191 0.981 1.429 1.744
beta0_pH[4,1] 1.578 0.216 1.102 1.596 1.960
beta0_pH[5,1] -0.859 0.314 -1.533 -0.831 -0.327
beta0_pH[6,1] -0.725 0.566 -2.119 -0.606 -0.015
beta0_pH[7,1] 0.184 0.682 -1.277 0.471 0.958
beta0_pH[8,1] -0.680 0.270 -1.274 -0.657 -0.212
beta0_pH[9,1] -0.650 0.287 -1.271 -0.637 -0.130
beta0_pH[10,1] 0.201 0.221 -0.252 0.206 0.625
beta0_pH[11,1] -0.070 0.176 -0.452 -0.054 0.248
beta0_pH[12,1] 0.502 0.182 0.142 0.504 0.858
beta0_pH[13,1] 0.013 0.143 -0.274 0.018 0.287
beta0_pH[14,1] -0.301 0.165 -0.635 -0.295 0.014
beta0_pH[15,1] -0.019 0.167 -0.354 -0.019 0.304
beta0_pH[16,1] -0.445 0.331 -1.185 -0.388 0.068
beta0_pH[1,2] 2.744 0.244 2.211 2.755 3.203
beta0_pH[2,2] 2.814 0.241 2.188 2.835 3.216
beta0_pH[3,2] 2.673 0.412 1.936 2.624 3.431
beta0_pH[4,2] 2.746 0.336 1.962 2.805 3.271
beta0_pH[5,2] 4.550 1.446 2.532 4.261 8.053
beta0_pH[6,2] 2.938 0.359 2.301 2.914 3.667
beta0_pH[7,2] 1.948 0.223 1.494 1.946 2.412
beta0_pH[8,2] 2.835 0.228 2.403 2.838 3.258
beta0_pH[9,2] 3.014 0.687 1.602 3.209 4.056
beta0_pH[10,2] 3.701 0.243 3.200 3.704 4.162
beta0_pH[11,2] -4.552 0.663 -5.391 -4.718 -2.748
beta0_pH[12,2] -4.776 0.455 -5.704 -4.779 -3.891
beta0_pH[13,2] -4.550 0.442 -5.418 -4.563 -3.646
beta0_pH[14,2] -5.631 0.558 -6.748 -5.638 -4.546
beta0_pH[15,2] -4.268 0.376 -5.001 -4.264 -3.540
beta0_pH[16,2] -4.847 0.434 -5.766 -4.837 -4.012
beta0_pH[1,3] 0.627 0.625 -0.820 0.760 1.419
beta0_pH[2,3] 2.003 0.376 0.896 2.097 2.453
beta0_pH[3,3] 2.302 0.311 1.524 2.380 2.734
beta0_pH[4,3] 2.764 0.401 1.603 2.863 3.208
beta0_pH[5,3] 1.202 1.782 -1.644 0.975 5.228
beta0_pH[6,3] -0.621 1.081 -2.915 -0.720 1.482
beta0_pH[7,3] -2.109 0.629 -3.599 -2.047 -1.073
beta0_pH[8,3] 0.270 0.193 -0.107 0.274 0.642
beta0_pH[9,3] -0.858 0.821 -3.056 -0.616 -0.028
beta0_pH[10,3] 0.014 0.968 -2.300 0.398 1.137
beta0_pH[11,3] -0.189 0.325 -0.829 -0.204 0.463
beta0_pH[12,3] -0.898 0.347 -1.615 -0.872 -0.271
beta0_pH[13,3] -0.112 0.334 -0.827 -0.112 0.554
beta0_pH[14,3] -0.277 0.254 -0.796 -0.273 0.201
beta0_pH[15,3] -0.733 0.306 -1.388 -0.716 -0.185
beta0_pH[16,3] -0.377 0.288 -0.929 -0.375 0.183
beta1_pH[1,1] 3.117 0.324 2.546 3.104 3.850
beta1_pH[2,1] 2.204 0.299 1.720 2.178 2.859
beta1_pH[3,1] 2.015 0.295 1.512 1.982 2.693
beta1_pH[4,1] 2.384 0.349 1.848 2.338 3.231
beta1_pH[5,1] 2.290 0.384 1.669 2.255 3.178
beta1_pH[6,1] 4.052 1.307 2.372 3.786 7.401
beta1_pH[7,1] 2.394 1.858 0.211 2.134 7.251
beta1_pH[8,1] 4.168 1.021 2.677 3.961 6.742
beta1_pH[9,1] 2.308 0.360 1.675 2.277 3.127
beta1_pH[10,1] 2.428 0.305 1.846 2.428 3.062
beta1_pH[11,1] 3.254 0.216 2.848 3.248 3.697
beta1_pH[12,1] 2.530 0.218 2.111 2.522 2.954
beta1_pH[13,1] 2.966 0.214 2.564 2.957 3.398
beta1_pH[14,1] 3.407 0.217 2.989 3.398 3.843
beta1_pH[15,1] 2.524 0.211 2.117 2.518 2.941
beta1_pH[16,1] 4.134 0.668 3.167 4.024 5.709
beta1_pH[1,2] 1.230 2.976 0.000 0.313 9.522
beta1_pH[2,2] 0.843 1.552 0.000 0.183 5.985
beta1_pH[3,2] 0.861 2.151 0.000 0.951 1.742
beta1_pH[4,2] 1.386 5.325 0.000 0.575 8.853
beta1_pH[5,2] 7.176 29.318 0.000 0.758 53.125
beta1_pH[6,2] 1.479 4.044 0.000 1.022 6.039
beta1_pH[7,2] 3.533 10.175 0.000 0.439 32.487
beta1_pH[8,2] 4.658 12.898 0.000 0.402 48.396
beta1_pH[9,2] 12.226 33.716 0.000 1.110 127.055
beta1_pH[10,2] 13.709 59.152 0.000 2.423 76.262
beta1_pH[11,2] 5.964 1.142 3.295 6.460 7.209
beta1_pH[12,2] 6.470 0.546 5.430 6.450 7.627
beta1_pH[13,2] 6.866 0.529 5.670 6.896 7.843
beta1_pH[14,2] 7.273 0.588 6.081 7.288 8.420
beta1_pH[15,2] 6.705 0.444 5.781 6.716 7.539
beta1_pH[16,2] 7.406 0.500 6.400 7.420 8.365
beta1_pH[1,3] 2.906 1.264 1.468 2.541 6.216
beta1_pH[2,3] 0.647 1.276 0.000 0.223 4.388
beta1_pH[3,3] 0.449 0.855 0.000 0.130 2.392
beta1_pH[4,3] 1.349 7.277 0.000 0.133 7.758
beta1_pH[5,3] 3.564 2.517 1.472 3.020 8.855
beta1_pH[6,3] 2.623 0.968 1.071 2.516 4.830
beta1_pH[7,3] 2.960 0.636 1.930 2.886 4.496
beta1_pH[8,3] 2.791 0.354 2.161 2.774 3.482
beta1_pH[9,3] 2.924 0.835 2.028 2.703 5.163
beta1_pH[10,3] 3.373 1.036 2.122 3.002 5.932
beta1_pH[11,3] 2.752 0.371 2.033 2.750 3.511
beta1_pH[12,3] 4.159 0.435 3.351 4.136 5.040
beta1_pH[13,3] 1.731 0.362 1.000 1.728 2.473
beta1_pH[14,3] 2.545 0.334 1.908 2.538 3.236
beta1_pH[15,3] 2.046 0.339 1.410 2.030 2.734
beta1_pH[16,3] 1.808 0.327 1.170 1.817 2.453
beta2_pH[1,1] 0.470 0.125 0.281 0.450 0.743
beta2_pH[2,1] 0.555 0.264 0.233 0.504 1.167
beta2_pH[3,1] 0.614 0.415 0.224 0.535 1.483
beta2_pH[4,1] 0.478 0.205 0.204 0.443 0.965
beta2_pH[5,1] 1.462 1.219 0.240 1.168 4.716
beta2_pH[6,1] 0.181 0.070 0.079 0.171 0.344
beta2_pH[7,1] -0.513 1.602 -4.886 0.022 1.818
beta2_pH[8,1] 0.234 0.081 0.124 0.219 0.437
beta2_pH[9,1] 0.443 0.200 0.195 0.402 0.926
beta2_pH[10,1] 0.593 0.265 0.291 0.533 1.225
beta2_pH[11,1] 0.797 0.219 0.485 0.761 1.341
beta2_pH[12,1] 1.358 0.492 0.739 1.267 2.479
beta2_pH[13,1] 0.750 0.224 0.421 0.718 1.269
beta2_pH[14,1] 0.835 0.199 0.532 0.805 1.314
beta2_pH[15,1] 0.810 0.282 0.425 0.761 1.467
beta2_pH[16,1] 0.367 0.171 0.168 0.319 0.822
beta2_pH[1,2] -4.689 7.967 -22.525 -3.971 9.259
beta2_pH[2,2] -5.107 7.666 -21.475 -4.368 8.956
beta2_pH[3,2] -5.781 7.096 -21.808 -4.830 8.249
beta2_pH[4,2] -5.723 6.943 -21.083 -4.732 6.979
beta2_pH[5,2] -7.504 5.885 -20.676 -7.260 3.413
beta2_pH[6,2] -8.356 5.119 -20.307 -8.622 -0.217
beta2_pH[7,2] -7.501 5.425 -20.638 -6.136 0.710
beta2_pH[8,2] -7.862 5.649 -20.763 -7.495 2.340
beta2_pH[9,2] -7.859 5.353 -20.049 -7.278 0.546
beta2_pH[10,2] -8.146 5.310 -20.784 -7.591 0.353
beta2_pH[11,2] -5.034 5.711 -16.872 -5.872 4.766
beta2_pH[12,2] -5.671 4.096 -15.898 -4.900 -0.781
beta2_pH[13,2] -5.612 3.788 -15.556 -4.529 -1.452
beta2_pH[14,2] -6.654 3.698 -16.628 -5.776 -2.077
beta2_pH[15,2] -7.870 3.620 -17.177 -7.180 -2.784
beta2_pH[16,2] -8.196 3.532 -17.191 -7.456 -3.380
beta2_pH[1,3] 3.442 5.093 0.123 0.680 18.459
beta2_pH[2,3] 2.030 6.640 -9.139 0.947 17.886
beta2_pH[3,3] 1.654 6.682 -8.984 0.189 18.268
beta2_pH[4,3] 2.171 6.667 -9.176 0.882 18.221
beta2_pH[5,3] 7.485 6.068 0.165 6.110 21.905
beta2_pH[6,3] 7.408 6.075 0.112 6.130 21.775
beta2_pH[7,3] 7.176 5.957 0.534 5.616 21.484
beta2_pH[8,3] 8.463 5.582 0.915 7.298 21.977
beta2_pH[9,3] 6.988 6.112 0.306 5.694 21.184
beta2_pH[10,3] 6.214 6.494 0.322 3.993 21.858
beta2_pH[11,3] -2.087 1.720 -6.406 -1.707 -0.633
beta2_pH[12,3] -2.179 1.555 -6.035 -1.797 -0.969
beta2_pH[13,3] -2.644 2.050 -8.787 -2.050 -0.794
beta2_pH[14,3] -2.577 1.905 -8.060 -2.014 -0.909
beta2_pH[15,3] -2.654 1.973 -8.885 -2.076 -1.055
beta2_pH[16,3] -2.729 2.102 -8.855 -2.095 -0.903
beta3_pH[1,1] 35.834 0.805 34.311 35.792 37.455
beta3_pH[2,1] 33.489 1.241 31.412 33.380 36.202
beta3_pH[3,1] 33.747 1.070 31.683 33.697 36.071
beta3_pH[4,1] 33.864 1.213 31.751 33.809 36.463
beta3_pH[5,1] 27.820 1.184 26.386 27.534 31.231
beta3_pH[6,1] 38.972 3.263 32.760 38.858 45.271
beta3_pH[7,1] 28.932 9.514 18.380 25.450 45.645
beta3_pH[8,1] 40.266 2.229 36.394 40.016 45.208
beta3_pH[9,1] 30.556 1.378 28.090 30.490 33.484
beta3_pH[10,1] 32.646 0.894 30.991 32.618 34.442
beta3_pH[11,1] 30.394 0.469 29.509 30.389 31.344
beta3_pH[12,1] 30.190 0.406 29.339 30.199 30.949
beta3_pH[13,1] 33.214 0.579 32.120 33.201 34.405
beta3_pH[14,1] 32.077 0.461 31.214 32.070 32.985
beta3_pH[15,1] 31.260 0.634 29.986 31.254 32.487
beta3_pH[16,1] 32.300 1.140 30.540 32.133 34.744
beta3_pH[1,2] 29.516 8.203 18.502 27.854 44.510
beta3_pH[2,2] 27.459 7.835 18.351 24.653 44.651
beta3_pH[3,2] 37.665 7.404 19.421 41.378 44.088
beta3_pH[4,2] 32.104 8.302 19.027 30.456 44.612
beta3_pH[5,2] 31.057 8.172 18.479 30.768 45.240
beta3_pH[6,2] 33.114 6.153 18.960 35.135 44.429
beta3_pH[7,2] 27.767 7.384 18.443 25.825 44.267
beta3_pH[8,2] 27.665 7.234 18.332 25.910 43.850
beta3_pH[9,2] 35.016 9.912 18.666 38.514 45.716
beta3_pH[10,2] 29.379 5.458 18.958 29.775 42.873
beta3_pH[11,2] 36.221 10.288 18.239 43.271 43.712
beta3_pH[12,2] 43.187 0.240 42.679 43.163 43.720
beta3_pH[13,2] 43.827 0.190 43.361 43.867 44.114
beta3_pH[14,2] 43.326 0.205 43.048 43.285 43.816
beta3_pH[15,2] 43.410 0.191 43.099 43.389 43.802
beta3_pH[16,2] 43.500 0.186 43.165 43.500 43.855
beta3_pH[1,3] 38.927 2.164 34.388 39.506 42.878
beta3_pH[2,3] 30.394 7.711 18.616 30.620 44.630
beta3_pH[3,3] 31.319 8.626 18.431 31.275 44.775
beta3_pH[4,3] 28.386 7.756 18.371 26.555 44.807
beta3_pH[5,3] 26.655 6.541 18.332 25.245 42.246
beta3_pH[6,3] 27.574 6.534 18.704 25.749 44.140
beta3_pH[7,3] 26.511 0.982 24.892 26.386 28.841
beta3_pH[8,3] 41.492 0.313 40.996 41.482 42.006
beta3_pH[9,3] 32.769 1.776 27.294 33.413 34.250
beta3_pH[10,3] 35.061 1.514 31.648 35.801 36.819
beta3_pH[11,3] 41.883 0.804 40.235 41.931 43.300
beta3_pH[12,3] 41.753 0.368 41.044 41.749 42.484
beta3_pH[13,3] 42.672 0.861 41.070 42.675 44.597
beta3_pH[14,3] 41.082 0.537 39.982 41.098 42.039
beta3_pH[15,3] 42.681 0.685 41.167 42.786 43.785
beta3_pH[16,3] 42.834 0.721 41.239 42.929 43.999
beta0_pelagic[1] 1.976 0.471 0.674 2.113 2.417
beta0_pelagic[2] 1.435 0.165 1.032 1.448 1.716
beta0_pelagic[3] 0.161 0.372 -0.708 0.220 0.730
beta0_pelagic[4] 0.102 0.713 -2.352 0.273 0.881
beta0_pelagic[5] 0.087 1.532 -3.378 0.968 1.462
beta0_pelagic[6] 1.032 0.713 -0.912 1.303 1.695
beta0_pelagic[7] 1.526 0.274 0.658 1.565 1.832
beta0_pelagic[8] 1.572 0.564 -0.292 1.703 1.973
beta0_pelagic[9] 1.729 1.432 -2.760 2.269 2.923
beta0_pelagic[10] 2.067 1.099 -1.313 2.499 2.779
beta0_pelagic[11] -0.083 0.672 -1.944 0.108 0.684
beta0_pelagic[12] 1.685 0.143 1.407 1.684 1.971
beta0_pelagic[13] 0.308 0.195 -0.114 0.319 0.656
beta0_pelagic[14] -0.100 0.253 -0.661 -0.074 0.332
beta0_pelagic[15] -0.257 0.132 -0.530 -0.259 0.000
beta0_pelagic[16] 0.378 0.196 -0.135 0.401 0.669
beta1_pelagic[1] 0.314 0.742 0.000 0.056 1.600
beta1_pelagic[2] 0.138 0.261 0.000 0.040 0.678
beta1_pelagic[3] 0.945 0.490 0.199 0.832 2.203
beta1_pelagic[4] 1.081 0.734 0.249 0.916 3.577
beta1_pelagic[5] 1.167 1.638 0.000 0.019 4.810
beta1_pelagic[6] 0.624 1.282 0.000 0.078 3.309
beta1_pelagic[7] 1.083 3.597 0.000 0.005 11.123
beta1_pelagic[8] 0.503 1.492 0.000 0.003 5.182
beta1_pelagic[9] 1.139 1.549 0.000 0.655 5.822
beta1_pelagic[10] 0.515 1.098 0.000 0.005 3.884
beta1_pelagic[11] 3.850 1.385 2.230 3.565 7.549
beta1_pelagic[12] 2.791 0.277 2.264 2.791 3.353
beta1_pelagic[13] 2.900 0.653 1.863 2.800 4.368
beta1_pelagic[14] 4.160 0.890 2.868 4.021 6.294
beta1_pelagic[15] 2.924 0.255 2.427 2.917 3.427
beta1_pelagic[16] 3.337 0.679 2.670 3.196 5.649
beta2_pelagic[1] 1.479 2.757 -4.659 1.309 7.068
beta2_pelagic[2] 1.494 2.689 -3.269 1.174 7.708
beta2_pelagic[3] 1.986 2.217 0.101 1.188 8.150
beta2_pelagic[4] 2.186 2.005 0.218 1.581 7.572
beta2_pelagic[5] -0.037 4.254 -7.232 -0.911 8.689
beta2_pelagic[6] 2.149 3.809 -6.420 2.175 9.428
beta2_pelagic[7] 0.523 4.525 -8.243 0.377 9.415
beta2_pelagic[8] 0.941 4.281 -7.899 0.758 9.070
beta2_pelagic[9] 1.843 3.685 -6.290 1.341 9.699
beta2_pelagic[10] 2.234 4.125 -7.118 2.740 8.216
beta2_pelagic[11] 1.278 2.063 0.082 0.261 7.130
beta2_pelagic[12] 5.084 2.634 1.526 4.534 11.961
beta2_pelagic[13] 0.679 0.776 0.201 0.454 2.552
beta2_pelagic[14] 0.322 0.122 0.174 0.297 0.628
beta2_pelagic[15] 5.150 2.069 1.657 5.066 10.388
beta2_pelagic[16] 4.567 2.901 0.237 4.343 11.364
beta3_pelagic[1] 27.679 7.506 18.395 25.159 44.656
beta3_pelagic[2] 30.250 8.107 18.545 29.302 44.979
beta3_pelagic[3] 30.048 4.770 22.114 29.761 42.497
beta3_pelagic[4] 25.213 2.775 19.257 25.433 30.557
beta3_pelagic[5] 34.984 9.872 18.782 35.514 45.989
beta3_pelagic[6] 29.854 6.749 18.727 29.519 44.079
beta3_pelagic[7] 28.493 8.170 18.387 27.066 44.728
beta3_pelagic[8] 28.288 7.947 18.379 26.268 44.627
beta3_pelagic[9] 28.530 6.716 18.876 26.708 43.465
beta3_pelagic[10] 27.995 8.305 18.210 26.051 44.647
beta3_pelagic[11] 41.932 2.264 35.968 42.784 45.101
beta3_pelagic[12] 43.455 0.241 43.020 43.448 43.921
beta3_pelagic[13] 42.728 1.267 40.287 42.652 45.297
beta3_pelagic[14] 42.043 1.625 38.756 42.085 45.178
beta3_pelagic[15] 43.193 0.211 42.678 43.196 43.576
beta3_pelagic[16] 43.255 0.410 42.365 43.243 44.206
mu_beta0_pelagic[1] 0.854 0.888 -1.078 0.900 2.520
mu_beta0_pelagic[2] 1.296 0.878 -0.944 1.524 2.465
mu_beta0_pelagic[3] 0.318 0.471 -0.642 0.336 1.233
tau_beta0_pelagic[1] 0.941 1.221 0.058 0.570 3.997
tau_beta0_pelagic[2] 2.003 3.854 0.082 1.058 8.666
tau_beta0_pelagic[3] 1.489 1.169 0.170 1.180 4.424
beta0_yellow[1] -0.539 0.184 -0.941 -0.520 -0.243
beta0_yellow[2] 0.499 0.162 0.174 0.505 0.783
beta0_yellow[3] -0.301 0.187 -0.659 -0.296 0.039
beta0_yellow[4] 0.849 0.249 0.244 0.882 1.189
beta0_yellow[5] -1.222 0.432 -2.064 -1.225 -0.379
beta0_yellow[6] 0.268 0.216 -0.169 0.271 0.683
beta0_yellow[7] 0.895 0.533 -1.027 1.030 1.318
beta0_yellow[8] 0.552 0.944 -1.642 0.908 1.276
beta0_yellow[9] -0.099 0.357 -0.707 -0.106 0.724
beta0_yellow[10] 0.230 0.155 -0.069 0.228 0.544
beta0_yellow[11] -2.945 1.511 -6.489 -2.303 -1.408
beta0_yellow[12] -3.731 0.443 -4.687 -3.708 -2.916
beta0_yellow[13] -3.845 0.510 -4.906 -3.821 -2.934
beta0_yellow[14] -2.101 0.709 -3.210 -2.219 -0.208
beta0_yellow[15] -2.977 0.529 -4.134 -2.952 -2.097
beta0_yellow[16] -2.474 0.514 -3.460 -2.479 -1.410
beta1_yellow[1] 0.671 1.224 0.000 0.362 4.709
beta1_yellow[2] 1.052 0.330 0.595 1.017 1.751
beta1_yellow[3] 0.656 0.312 0.070 0.645 1.182
beta1_yellow[4] 1.318 0.717 0.621 1.155 3.407
beta1_yellow[5] 3.018 1.489 1.320 2.837 5.409
beta1_yellow[6] 2.279 0.358 1.598 2.274 2.992
beta1_yellow[7] 5.454 5.188 0.538 4.110 25.326
beta1_yellow[8] 2.304 5.905 0.009 1.749 6.929
beta1_yellow[9] 3.113 7.971 0.861 1.589 32.796
beta1_yellow[10] 2.379 0.493 1.555 2.350 3.386
beta1_yellow[11] 3.036 1.440 1.586 2.439 6.454
beta1_yellow[12] 2.535 0.455 1.709 2.503 3.508
beta1_yellow[13] 2.987 0.523 2.065 2.958 4.109
beta1_yellow[14] 2.212 0.641 0.586 2.282 3.298
beta1_yellow[15] 2.212 0.536 1.319 2.179 3.367
beta1_yellow[16] 2.233 0.506 1.170 2.245 3.201
beta2_yellow[1] -3.142 3.029 -10.063 -2.709 2.036
beta2_yellow[2] -3.389 2.629 -10.073 -2.845 -0.228
beta2_yellow[3] -3.454 2.472 -8.766 -3.046 -0.156
beta2_yellow[4] -3.002 2.779 -9.817 -2.156 -0.122
beta2_yellow[5] -4.378 2.859 -11.130 -3.920 -0.584
beta2_yellow[6] 3.523 2.149 0.918 2.940 8.934
beta2_yellow[7] -4.015 3.716 -11.519 -3.975 4.932
beta2_yellow[8] -1.678 4.424 -10.813 -1.592 7.919
beta2_yellow[9] 3.186 3.286 -5.601 3.127 9.629
beta2_yellow[10] -4.566 2.743 -11.076 -4.027 -0.798
beta2_yellow[11] -1.023 4.175 -7.177 -2.318 7.150
beta2_yellow[12] -4.342 2.382 -10.399 -3.810 -1.250
beta2_yellow[13] -4.244 2.193 -10.122 -3.738 -1.456
beta2_yellow[14] -4.151 2.551 -10.609 -3.740 -0.298
beta2_yellow[15] -3.212 3.009 -9.912 -2.976 4.408
beta2_yellow[16] -4.388 2.341 -10.137 -3.882 -1.354
beta3_yellow[1] 27.021 7.510 18.269 24.271 44.154
beta3_yellow[2] 29.141 1.635 26.576 28.921 32.562
beta3_yellow[3] 32.934 3.091 25.383 32.894 39.349
beta3_yellow[4] 29.334 3.544 22.330 28.181 35.959
beta3_yellow[5] 33.360 1.446 30.648 33.402 35.941
beta3_yellow[6] 39.678 0.548 38.716 39.635 40.927
beta3_yellow[7] 20.778 2.953 18.534 20.100 29.495
beta3_yellow[8] 24.887 5.814 18.311 23.596 42.224
beta3_yellow[9] 36.742 4.418 19.143 37.539 42.445
beta3_yellow[10] 29.310 0.633 27.852 29.396 30.101
beta3_yellow[11] 39.823 7.859 28.121 45.092 45.958
beta3_yellow[12] 43.340 0.395 42.538 43.297 44.166
beta3_yellow[13] 44.888 0.374 44.041 44.953 45.515
beta3_yellow[14] 43.493 3.038 32.424 44.211 45.799
beta3_yellow[15] 44.194 4.030 28.512 45.227 45.971
beta3_yellow[16] 44.597 0.628 43.475 44.596 45.801
mu_beta0_yellow[1] 0.108 0.552 -1.051 0.119 1.240
mu_beta0_yellow[2] 0.094 0.502 -0.949 0.108 1.060
mu_beta0_yellow[3] -2.545 0.714 -3.660 -2.652 -0.734
tau_beta0_yellow[1] 1.802 2.352 0.093 1.161 7.393
tau_beta0_yellow[2] 1.409 1.839 0.140 1.002 4.841
tau_beta0_yellow[3] 1.611 3.743 0.065 0.783 7.585
beta0_black[1] 0.099 0.196 -0.317 0.122 0.435
beta0_black[2] 1.878 0.147 1.547 1.886 2.144
beta0_black[3] 1.306 0.143 1.024 1.308 1.568
beta0_black[4] 2.021 0.393 1.072 2.049 2.569
beta0_black[5] 1.575 1.993 -2.713 1.643 5.658
beta0_black[6] 1.580 1.967 -2.840 1.634 5.702
beta0_black[7] 1.618 2.017 -2.781 1.656 5.881
beta0_black[8] 1.256 0.242 0.760 1.263 1.702
beta0_black[9] 2.418 0.276 1.870 2.428 2.910
beta0_black[10] 1.462 0.134 1.185 1.463 1.724
beta0_black[11] 3.449 0.253 3.086 3.470 3.771
beta0_black[12] 4.471 0.195 4.083 4.473 4.848
beta0_black[13] 0.354 0.470 -0.430 0.306 1.120
beta0_black[14] 1.963 0.814 -0.490 2.186 2.901
beta0_black[15] 1.290 0.166 0.965 1.295 1.598
beta0_black[16] 4.166 0.565 2.747 4.251 4.570
beta2_black[1] 0.931 3.367 -5.749 1.082 7.892
beta2_black[2] -0.627 3.334 -7.598 -0.566 6.272
beta2_black[3] -0.249 3.429 -7.670 -0.236 6.605
beta2_black[4] -1.687 3.072 -8.534 -1.428 6.406
beta2_black[5] -0.056 3.306 -6.861 -0.064 7.023
beta2_black[6] -0.112 3.375 -6.894 -0.057 6.643
beta2_black[7] -0.070 3.323 -6.940 -0.042 6.644
beta2_black[8] -0.444 3.444 -7.510 -0.491 6.517
beta2_black[9] -0.072 3.364 -7.089 -0.059 6.682
beta2_black[10] -0.189 3.404 -7.122 -0.096 6.324
beta2_black[11] -0.970 1.815 -4.306 -1.005 2.511
beta2_black[12] -2.355 1.751 -7.249 -1.916 -0.363
beta2_black[13] -1.848 2.053 -6.860 -1.570 2.353
beta2_black[14] -1.205 1.648 -5.975 -0.590 -0.039
beta2_black[15] -1.030 2.552 -6.389 -1.069 4.761
beta2_black[16] -0.897 2.531 -6.339 -0.927 4.638
beta3_black[1] 34.189 8.411 18.908 36.681 44.492
beta3_black[2] 30.288 7.983 18.458 29.822 44.865
beta3_black[3] 30.257 8.020 18.511 29.552 44.881
beta3_black[4] 32.333 4.661 20.004 32.740 41.715
beta3_black[5] 30.032 7.961 18.411 29.156 45.046
beta3_black[6] 29.882 7.889 18.467 28.899 44.861
beta3_black[7] 30.121 8.050 18.435 29.177 45.115
beta3_black[8] 29.666 7.951 18.570 28.279 44.688
beta3_black[9] 30.081 7.970 18.436 29.312 44.685
beta3_black[10] 29.599 8.007 18.510 28.202 44.819
beta3_black[11] 30.758 7.851 18.636 30.517 44.964
beta3_black[12] 32.255 1.861 26.617 32.765 33.815
beta3_black[13] 36.530 6.001 19.909 39.085 43.101
beta3_black[14] 36.758 5.545 20.937 38.183 44.504
beta3_black[15] 31.373 7.960 18.610 31.348 45.265
beta3_black[16] 30.916 7.945 18.529 30.647 44.971
beta4_black[1] -0.274 0.190 -0.645 -0.274 0.104
beta4_black[2] 0.251 0.178 -0.105 0.253 0.589
beta4_black[3] -0.937 0.190 -1.306 -0.936 -0.565
beta4_black[4] 0.538 0.227 0.084 0.537 0.971
beta4_black[5] 0.210 2.362 -4.125 0.113 4.986
beta4_black[6] 0.276 2.424 -4.288 0.211 5.141
beta4_black[7] 0.260 2.462 -4.357 0.162 5.492
beta4_black[8] -0.693 0.369 -1.420 -0.691 0.030
beta4_black[9] 1.447 0.990 -0.083 1.311 3.750
beta4_black[10] 0.023 0.181 -0.341 0.023 0.380
beta4_black[11] -0.691 0.209 -1.106 -0.690 -0.284
beta4_black[12] 0.301 0.334 -0.314 0.292 0.979
beta4_black[13] -1.200 0.215 -1.612 -1.207 -0.771
beta4_black[14] -0.118 0.236 -0.559 -0.120 0.343
beta4_black[15] -0.894 0.208 -1.308 -0.893 -0.477
beta4_black[16] -0.596 0.215 -1.031 -0.590 -0.172
mu_beta0_black[1] 1.225 0.803 -0.565 1.258 2.791
mu_beta0_black[2] 1.589 0.888 -0.560 1.646 3.327
mu_beta0_black[3] 2.414 0.953 0.369 2.459 4.258
tau_beta0_black[1] 0.943 0.954 0.064 0.651 3.544
tau_beta0_black[2] 2.020 4.140 0.059 0.875 10.580
tau_beta0_black[3] 0.302 0.222 0.055 0.245 0.863
beta0_dsr[11] -2.887 0.277 -3.444 -2.883 -2.343
beta0_dsr[12] 4.528 0.280 4.002 4.528 5.087
beta0_dsr[13] -1.354 0.324 -1.998 -1.339 -0.802
beta0_dsr[14] -3.709 0.516 -4.735 -3.700 -2.729
beta0_dsr[15] -1.943 0.279 -2.475 -1.946 -1.389
beta0_dsr[16] -2.994 0.355 -3.698 -2.990 -2.299
beta1_dsr[11] 4.822 0.291 4.263 4.817 5.407
beta1_dsr[12] 9.432 41.180 2.325 5.109 22.573
beta1_dsr[13] 2.876 0.386 2.293 2.852 3.559
beta1_dsr[14] 6.373 0.543 5.336 6.365 7.469
beta1_dsr[15] 3.342 0.287 2.771 3.352 3.912
beta1_dsr[16] 5.813 0.368 5.104 5.806 6.550
beta2_dsr[11] -8.281 2.363 -13.970 -7.929 -4.675
beta2_dsr[12] -7.029 2.623 -13.013 -6.765 -2.252
beta2_dsr[13] -6.330 2.746 -12.280 -6.208 -1.275
beta2_dsr[14] -6.135 2.697 -11.887 -5.939 -1.800
beta2_dsr[15] -7.738 2.327 -13.087 -7.491 -4.012
beta2_dsr[16] -7.899 2.367 -13.651 -7.548 -4.354
beta3_dsr[11] 43.489 0.147 43.215 43.488 43.769
beta3_dsr[12] 33.980 0.690 32.124 34.129 34.820
beta3_dsr[13] 43.239 0.346 42.790 43.194 43.859
beta3_dsr[14] 43.351 0.240 43.073 43.277 43.948
beta3_dsr[15] 43.509 0.188 43.164 43.507 43.844
beta3_dsr[16] 43.445 0.157 43.179 43.433 43.757
beta4_dsr[11] 0.579 0.209 0.175 0.580 0.996
beta4_dsr[12] 0.237 0.438 -0.633 0.237 1.124
beta4_dsr[13] -0.173 0.214 -0.587 -0.168 0.247
beta4_dsr[14] 0.147 0.245 -0.321 0.150 0.609
beta4_dsr[15] 0.723 0.211 0.316 0.723 1.138
beta4_dsr[16] 0.144 0.226 -0.290 0.142 0.604
beta0_slope[11] -1.941 0.161 -2.254 -1.944 -1.616
beta0_slope[12] -4.666 0.264 -5.197 -4.662 -4.151
beta0_slope[13] -1.345 0.213 -1.830 -1.332 -0.984
beta0_slope[14] -2.634 0.179 -2.994 -2.637 -2.289
beta0_slope[15] -1.377 0.167 -1.695 -1.378 -1.044
beta0_slope[16] -2.726 0.173 -3.072 -2.728 -2.392
beta1_slope[11] 4.595 0.293 4.036 4.588 5.185
beta1_slope[12] 5.008 0.516 3.971 4.994 6.057
beta1_slope[13] 2.938 0.541 2.241 2.865 4.483
beta1_slope[14] 6.535 0.553 5.486 6.520 7.682
beta1_slope[15] 3.052 0.285 2.498 3.056 3.614
beta1_slope[16] 5.378 0.389 4.633 5.369 6.149
beta2_slope[11] 8.106 2.366 4.477 7.804 13.775
beta2_slope[12] 7.161 2.462 2.865 6.934 12.600
beta2_slope[13] 5.701 2.975 0.364 5.745 11.812
beta2_slope[14] 6.641 2.440 2.443 6.477 12.221
beta2_slope[15] 7.590 2.425 3.689 7.303 13.194
beta2_slope[16] 7.687 2.383 4.087 7.343 13.149
beta3_slope[11] 43.477 0.152 43.205 43.473 43.778
beta3_slope[12] 43.416 0.230 43.077 43.386 43.877
beta3_slope[13] 43.652 0.442 42.937 43.721 44.397
beta3_slope[14] 43.322 0.177 43.092 43.278 43.772
beta3_slope[15] 43.515 0.195 43.156 43.511 43.871
beta3_slope[16] 43.459 0.172 43.169 43.447 43.815
beta4_slope[11] -0.578 0.215 -1.010 -0.574 -0.167
beta4_slope[12] -1.394 0.644 -2.856 -1.322 -0.357
beta4_slope[13] 0.049 0.219 -0.374 0.054 0.490
beta4_slope[14] -0.179 0.263 -0.689 -0.181 0.356
beta4_slope[15] -0.720 0.216 -1.150 -0.720 -0.302
beta4_slope[16] -0.191 0.229 -0.645 -0.191 0.264
sigma_H[1] 0.196 0.054 0.099 0.194 0.308
sigma_H[2] 0.172 0.030 0.118 0.170 0.235
sigma_H[3] 0.196 0.042 0.119 0.194 0.282
sigma_H[4] 0.421 0.078 0.294 0.412 0.593
sigma_H[5] 0.991 0.212 0.584 0.986 1.424
sigma_H[6] 0.394 0.199 0.042 0.387 0.815
sigma_H[7] 0.299 0.061 0.205 0.291 0.437
sigma_H[8] 0.414 0.091 0.274 0.406 0.598
sigma_H[9] 0.527 0.128 0.332 0.510 0.828
sigma_H[10] 0.215 0.042 0.142 0.213 0.307
sigma_H[11] 0.278 0.045 0.205 0.274 0.377
sigma_H[12] 0.435 0.166 0.209 0.406 0.768
sigma_H[13] 0.214 0.037 0.149 0.211 0.294
sigma_H[14] 0.510 0.092 0.347 0.501 0.711
sigma_H[15] 0.246 0.040 0.177 0.242 0.336
sigma_H[16] 0.224 0.043 0.150 0.220 0.320
lambda_H[1] 3.073 3.920 0.160 1.766 13.216
lambda_H[2] 8.305 7.470 0.799 6.219 29.319
lambda_H[3] 6.029 8.910 0.289 2.996 31.503
lambda_H[4] 0.006 0.004 0.001 0.005 0.017
lambda_H[5] 3.405 7.019 0.037 0.992 22.506
lambda_H[6] 7.699 15.141 0.008 1.235 47.855
lambda_H[7] 0.014 0.010 0.002 0.011 0.038
lambda_H[8] 7.896 10.066 0.090 4.512 34.940
lambda_H[9] 0.015 0.010 0.003 0.013 0.040
lambda_H[10] 0.317 0.607 0.032 0.204 1.186
lambda_H[11] 0.256 0.370 0.012 0.126 1.290
lambda_H[12] 4.844 6.155 0.175 2.771 20.536
lambda_H[13] 3.468 3.169 0.235 2.552 11.964
lambda_H[14] 3.353 4.171 0.234 2.031 15.062
lambda_H[15] 0.026 0.038 0.003 0.017 0.100
lambda_H[16] 0.795 1.099 0.044 0.415 3.790
mu_lambda_H[1] 4.364 1.929 1.240 4.164 8.612
mu_lambda_H[2] 3.868 1.978 0.598 3.694 8.007
mu_lambda_H[3] 3.450 1.814 0.754 3.166 7.558
sigma_lambda_H[1] 8.694 4.407 1.969 8.009 18.357
sigma_lambda_H[2] 8.345 4.632 0.949 7.825 18.341
sigma_lambda_H[3] 6.192 3.945 0.992 5.330 16.183
beta_H[1,1] 6.927 1.056 4.477 7.112 8.602
beta_H[2,1] 9.888 0.505 8.804 9.923 10.763
beta_H[3,1] 8.000 0.774 6.199 8.091 9.260
beta_H[4,1] 9.317 7.952 -6.964 9.633 24.415
beta_H[5,1] 0.150 2.261 -4.650 0.272 4.187
beta_H[6,1] 3.193 4.040 -7.238 4.632 7.570
beta_H[7,1] 0.784 5.821 -11.788 1.178 11.172
beta_H[8,1] 1.440 3.912 -2.302 1.291 3.512
beta_H[9,1] 13.048 5.770 1.723 12.970 24.251
beta_H[10,1] 7.113 1.695 3.545 7.177 10.431
beta_H[11,1] 4.991 3.537 -2.964 5.691 9.866
beta_H[12,1] 2.605 1.072 0.790 2.530 5.023
beta_H[13,1] 9.064 0.953 7.256 9.126 10.577
beta_H[14,1] 2.173 1.065 0.115 2.164 4.218
beta_H[15,1] -6.099 3.813 -12.956 -6.295 2.090
beta_H[16,1] 3.419 2.697 -1.013 3.108 9.805
beta_H[1,2] 7.914 0.240 7.427 7.919 8.382
beta_H[2,2] 10.027 0.136 9.759 10.026 10.298
beta_H[3,2] 8.946 0.202 8.544 8.943 9.348
beta_H[4,2] 3.573 1.513 0.722 3.502 6.768
beta_H[5,2] 1.962 0.918 0.148 1.963 3.721
beta_H[6,2] 5.747 1.056 3.256 5.926 7.386
beta_H[7,2] 2.557 1.105 0.588 2.488 4.871
beta_H[8,2] 2.999 1.131 1.266 3.153 4.261
beta_H[9,2] 3.494 1.112 1.382 3.445 5.725
beta_H[10,2] 8.186 0.338 7.482 8.199 8.837
beta_H[11,2] 9.790 0.633 8.844 9.667 11.174
beta_H[12,2] 3.940 0.364 3.247 3.934 4.682
beta_H[13,2] 9.122 0.252 8.682 9.109 9.625
beta_H[14,2] 4.006 0.358 3.331 3.997 4.759
beta_H[15,2] 11.356 0.687 9.849 11.384 12.590
beta_H[16,2] 4.518 0.826 2.974 4.501 6.164
beta_H[1,3] 8.473 0.238 8.050 8.454 8.968
beta_H[2,3] 10.068 0.119 9.835 10.065 10.307
beta_H[3,3] 9.613 0.164 9.305 9.606 9.953
beta_H[4,3] -2.490 0.900 -4.310 -2.463 -0.793
beta_H[5,3] 3.824 0.614 2.563 3.819 5.001
beta_H[6,3] 7.971 1.196 6.372 7.582 10.599
beta_H[7,3] -2.644 0.719 -4.067 -2.641 -1.229
beta_H[8,3] 5.253 0.519 4.651 5.186 6.199
beta_H[9,3] -2.836 0.758 -4.328 -2.808 -1.363
beta_H[10,3] 8.708 0.273 8.192 8.706 9.246
beta_H[11,3] 8.532 0.288 7.916 8.554 9.039
beta_H[12,3] 5.248 0.329 4.482 5.287 5.768
beta_H[13,3] 8.842 0.174 8.489 8.850 9.175
beta_H[14,3] 5.704 0.280 5.070 5.728 6.202
beta_H[15,3] 10.368 0.318 9.755 10.365 10.974
beta_H[16,3] 6.220 0.594 4.917 6.285 7.208
beta_H[1,4] 8.272 0.173 7.918 8.281 8.583
beta_H[2,4] 10.135 0.121 9.875 10.140 10.355
beta_H[3,4] 10.108 0.164 9.752 10.120 10.384
beta_H[4,4] 11.793 0.458 10.853 11.811 12.681
beta_H[5,4] 5.498 0.764 4.254 5.417 7.197
beta_H[6,4] 7.077 0.924 4.943 7.374 8.307
beta_H[7,4] 8.198 0.353 7.503 8.201 8.865
beta_H[8,4] 6.709 0.261 6.218 6.720 7.161
beta_H[9,4] 7.202 0.472 6.284 7.194 8.142
beta_H[10,4] 7.754 0.234 7.328 7.749 8.257
beta_H[11,4] 9.386 0.202 8.995 9.388 9.788
beta_H[12,4] 7.138 0.214 6.719 7.135 7.581
beta_H[13,4] 9.042 0.141 8.762 9.043 9.307
beta_H[14,4] 7.729 0.220 7.298 7.726 8.176
beta_H[15,4] 9.463 0.238 8.990 9.467 9.925
beta_H[16,4] 9.356 0.239 8.925 9.344 9.845
beta_H[1,5] 8.983 0.145 8.679 8.986 9.249
beta_H[2,5] 10.782 0.092 10.602 10.779 10.973
beta_H[3,5] 10.920 0.172 10.623 10.903 11.295
beta_H[4,5] 8.372 0.470 7.468 8.354 9.347
beta_H[5,5] 5.406 0.580 4.124 5.451 6.418
beta_H[6,5] 8.789 0.611 7.938 8.629 10.299
beta_H[7,5] 6.809 0.339 6.163 6.809 7.479
beta_H[8,5] 8.219 0.220 7.859 8.206 8.641
beta_H[9,5] 8.208 0.482 7.271 8.211 9.157
beta_H[10,5] 10.077 0.231 9.605 10.080 10.531
beta_H[11,5] 11.519 0.230 11.070 11.519 11.967
beta_H[12,5] 8.484 0.192 8.106 8.482 8.852
beta_H[13,5] 10.009 0.132 9.754 10.009 10.273
beta_H[14,5] 9.198 0.235 8.754 9.184 9.681
beta_H[15,5] 11.169 0.248 10.702 11.162 11.655
beta_H[16,5] 9.916 0.175 9.556 9.918 10.246
beta_H[1,6] 10.183 0.189 9.860 10.170 10.616
beta_H[2,6] 11.513 0.106 11.304 11.513 11.726
beta_H[3,6] 10.812 0.164 10.459 10.824 11.105
beta_H[4,6] 12.910 0.820 11.223 12.920 14.475
beta_H[5,6] 5.887 0.594 4.701 5.884 7.071
beta_H[6,6] 8.788 0.666 7.043 8.913 9.733
beta_H[7,6] 9.810 0.565 8.698 9.825 10.908
beta_H[8,6] 9.514 0.285 9.005 9.535 9.953
beta_H[9,6] 8.469 0.802 6.906 8.440 10.133
beta_H[10,6] 9.513 0.315 8.811 9.542 10.051
beta_H[11,6] 10.808 0.354 10.052 10.835 11.453
beta_H[12,6] 9.380 0.247 8.913 9.373 9.896
beta_H[13,6] 11.043 0.165 10.755 11.032 11.392
beta_H[14,6] 9.824 0.287 9.274 9.825 10.384
beta_H[15,6] 10.828 0.427 10.005 10.830 11.683
beta_H[16,6] 10.537 0.234 10.048 10.549 10.989
beta_H[1,7] 10.876 0.874 8.764 10.990 12.271
beta_H[2,7] 12.223 0.426 11.358 12.220 13.084
beta_H[3,7] 10.541 0.668 9.083 10.618 11.671
beta_H[4,7] 2.343 4.185 -5.860 2.290 10.672
beta_H[5,7] 6.471 1.859 3.168 6.408 10.616
beta_H[6,7] 9.665 2.316 5.047 9.575 15.760
beta_H[7,7] 10.714 2.807 5.347 10.631 16.409
beta_H[8,7] 10.976 1.002 9.495 10.925 12.654
beta_H[9,7] 4.458 4.097 -3.735 4.490 12.292
beta_H[10,7] 9.798 1.443 7.181 9.712 12.997
beta_H[11,7] 11.000 1.725 7.809 10.903 14.776
beta_H[12,7] 9.987 0.932 7.930 10.060 11.620
beta_H[13,7] 11.657 0.760 9.893 11.743 12.865
beta_H[14,7] 10.380 0.983 8.329 10.438 12.133
beta_H[15,7] 12.024 2.238 7.620 12.016 16.308
beta_H[16,7] 12.307 1.272 10.135 12.154 15.257
beta0_H[1] 9.044 12.860 -18.274 9.180 35.968
beta0_H[2] 10.747 6.394 -2.277 10.746 23.889
beta0_H[3] 10.262 9.936 -8.615 10.065 30.993
beta0_H[4] 6.209 187.970 -372.485 6.826 393.697
beta0_H[5] 4.578 24.037 -41.247 3.989 54.107
beta0_H[6] 8.743 50.129 -97.954 7.854 118.928
beta0_H[7] 2.040 132.649 -273.726 5.352 256.227
beta0_H[8] 5.459 32.585 -19.406 6.255 27.822
beta0_H[9] 6.149 118.564 -237.652 8.836 242.016
beta0_H[10] 7.419 34.241 -64.902 7.880 76.700
beta0_H[11] 8.986 51.350 -101.605 9.782 116.250
beta0_H[12] 6.882 12.151 -16.362 6.776 29.203
beta0_H[13] 9.931 11.096 -11.896 10.026 29.515
beta0_H[14] 7.354 11.385 -16.067 7.395 31.136
beta0_H[15] 9.035 105.528 -203.529 11.013 220.757
beta0_H[16] 8.421 25.043 -43.052 8.143 58.462